U.S. patent application number 11/222023 was filed with the patent office on 2008-01-24 for energy absorbent material.
This patent application is currently assigned to University of Washington. Invention is credited to Minoru Taya, Ying Zhao.
Application Number | 20080020229 11/222023 |
Document ID | / |
Family ID | 36036962 |
Filed Date | 2008-01-24 |
United States Patent
Application |
20080020229 |
Kind Code |
A1 |
Taya; Minoru ; et
al. |
January 24, 2008 |
Energy absorbent material
Abstract
A method for making a ductile and porous shape memory alloy
(SMA) using spark plasma sintering, and an energy absorbing
structure including a ductile and porous SMA are disclosed. In an
exemplary structure, an SMA spring encompasses a generally
cylindrical energy absorbing material. The function of the SMA
spring is to resist the bulging of the cylinder under large
compressive loading, thereby increasing a buckling load that the
cylindrical energy absorbing material can accommodate. The SMA
spring also contributes to the resistance of the energy absorbing
structure to an initial compressive loading. Preferably, the
cylinder is formed of ductile, porous and super elastic SMA. A
working prototype includes a NiTi spring, and a porous NiTi
cylinder or rod.
Inventors: |
Taya; Minoru; (Mercer
Island, WA) ; Zhao; Ying; (Seattle, WA) |
Correspondence
Address: |
LAW OFFICES OF RONALD M ANDERSON
600 108TH AVE, NE
SUITE 507
BELLEVUE
WA
98004
US
|
Assignee: |
University of Washington
Seattle
WA
|
Family ID: |
36036962 |
Appl. No.: |
11/222023 |
Filed: |
September 8, 2005 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
|
60608395 |
Sep 8, 2004 |
|
|
|
Current U.S.
Class: |
428/613 ;
419/2 |
Current CPC
Class: |
C25D 5/18 20130101; Y10T
428/12479 20150115; C25D 3/562 20130101; C25D 5/48 20130101 |
Class at
Publication: |
428/613 ;
419/002 |
International
Class: |
B22F 3/11 20060101
B22F003/11; B32B 5/18 20060101 B32B005/18 |
Goverment Interests
GOVERNMENT RIGHTS
[0002] This invention was funded at least in part with a grant (No.
N-000140210666) from the ONR, and the U.S. government may have
certain rights in this invention.
Claims
1.-8. (canceled)
9. An energy absorbing structure comprising a first shape memory
alloy (SMA) member and a second SMA member, wherein the first SMA
member is disposed externally of the second SMA member and is
configured to constrain the second SMA member so as to increase a
buckling load that the second SMA member can accommodate, the
second SMA member comprising a super elastic and ductile SMA
exhibiting a porous microstructure in which interstitial spaces
separate adjacent SMA particles.
10. The energy absorbing structure of claim 9, wherein the first
SMA member and the second SMA member are coaxially aligned.
11. The energy absorbing structure of claim 9, further comprising a
plurality of first SMA members, each disposed to constrain the
second SMA member.
12. The energy absorbing structure of claim 9, wherein the first
SMA member comprises a spring.
13. (canceled)
14. (canceled)
15. The energy absorbing structure of claim 9, wherein an initial
load applied to the energy absorbing structure is borne by the
first SMA member.
16. The energy absorbing structure of claim 9, wherein deformation
of the first SMA member under a load exposes the second SMA member
to the load.
17. The energy absorbing structure of claim 9, wherein deformation
of the second SMA member under a load causes the second SMA member
to contact the first SMA member.
18. The energy absorbing structure of claim 9, wherein the first
SMA member is configured to elastically deform under relatively
smaller loads, and to constrain the second SMA member only under
relatively larger loads.
19. (canceled)
20. The energy absorbing structure of claim 9, wherein the first
SMA members are SMA member is super elastic.
21. The energy absorbing structure of claim 9, wherein the first
and second SMA members comprise an alloy that includes nickel and
titanium.
22. An energy absorbing structure comprising a plurality of first
members and a second member, wherein the first member is plurality
of first members are configured to constrain the second member, to
increase a buckling load that the second member can accommodate,
wherein the second member comprises a ductile and porous shape
memory alloy (SMA), and wherein the plurality of first members are
distributed about a periphery of the second member, such that the
plurality of first members do not share a common central axis.
23. The energy absorbing structure of claim 22, wherein the second
member comprises a super elastic alloy that includes nickel and
titanium.
24. An energy absorbing structure comprising: (a) a porous shape
memory alloy (SMA) member; and (b) a constraining member configured
to selectively constrain the porous SMA member so as to increase a
buckling load that the porous SMA member can accommodate wherein
the constraining member is configured to elastically deform under
relatively smaller loads, and to constrain the porous SMA member
under relatively larger loads, a spacing between the constraining
member and the porous SMA member having been selected such that a
gap exists between the constraining member and the porous SMA
member when the porous SMA member is unloaded, but no gap exists
when the porous SMA member is experiencing relatively greater
loads.
25. (canceled)
Description
RELATED APPLICATIONS
[0001] This application is based on a prior copending provisional
application, Ser. No. 60/608,395, filed on Sep. 8, 2004, the
benefit of the filing date of which is hereby claimed under 35
U.S.C. .sctn.119(e).
BACKGROUND
[0003] Over the last two decades, shape memory alloys (SMA) have
attracted great interest as materials that could be beneficially
employed in a wide variety of applications, including aerospace
applications, naval applications, automotive applications, and
medical applications. NiTi alloy is one of the more frequently used
SMAs, due to its large flow stress and shape memory effect strain.
Recently, porous NiTi has been considered for incorporation into
medical implants, and as a high energy absorption structural
material. While the properties of porous NiTi are intriguing,
fabrication of porous NiTi is challenging. One prior art technique
for fabricating porous NiTi is based on a combustion synthesis.
However, studies have indicated porous NiTi synthesized by this
method is brittle. Another fabrication method that has been
investigated involves powder sintering; however, studies have
indicated that porous NiTi fabricated using powder sintering is
also brittle, and lacks a stress plateau in the stress-strain
curve. A self-propagating high temperature synthesis (SHS) is a
further technique that can be used to produce porous NiTi; yet
again, the porous NiTi fabricated using SHS is undesirably brittle.
Still another technique disclosed in the prior art employs a hot
isostatic press (HIP), which also yields a brittle porous NiTi.
[0004] It would be desirable to provide techniques for fabricating
porous NiTi that exhibits a higher ductility, i.e., which is not
brittle. It would further be desirable to provide a new energy
absorbing structure based on the properties of porous SMA, such as
NiTi.
SUMMARY
[0005] In order to achieve a porous SMA exhibiting a higher
ductility than available using prior art methods, a spark plasma
sintering (SPS) method is disclosed herein. NiTi raw powders
(preferably of super-elastic grade) are loaded into a graphite die
and pressed to a desired pressure. A current is then induced
through the die and stacked powder particles. The current activates
the powder particles to a high energy state, and neck formation
easily occurs at relatively low temperatures, in a relatively short
period of time, as compared with conventional sintering techniques
(such as hot press, HIP or SHS techniques). Moreover, the spark
discharge purifies the surface of the powder particles, which
enhances neck formation, and the generation of high quality
sintered materials. Empirical studies have indicated that the SPS
technique can achieve a porous NiTi exhibiting greater ductility
than achievable using other methods disclosed in the prior art.
[0006] In at least one embodiment, the raw NiTi powder comprises
50.9% nickel and 49.1% titanium. While empirical studies have
focused on using the SPS technique with NiTi powders, it should be
understood that the SPS technique disclosed herein can also be used
to achieve high quality SMA alloys made from other materials.
[0007] The disclosure provided herein is further directed to an
energy absorbing structure including a porous and ductile SMA. The
energy absorbing structure includes a super elastic grade SMA
component, and a porous and ductile SMA portion. In at least one
embodiment the porous and ductile SMA is NiTi. Significantly, the
porosity of the porous and ductile SMA portion enables a relatively
lightweight structure to be achieved, while the energy absorbing
properties of the porous and ductile SMA portion enhance the energy
absorbing capability of the structure.
[0008] Such an energy absorbing structure can be achieved by
combining a (preferably super elastic) NiTi spring with a porous
and ductile NiTi bar or rod, such that the spring and bar are
coaxial, with the spring encompassing the bar. The spring acts as a
constraint to increase the bar's ability to accommodate a buckling
load. This arrangement enables the energy absorbing structure to
exhibit a desirable force displacement relationship. During a
modest initial loading, a majority of the load is carried by the
spring, and the force displacement curve is generally linear. As
the load increases, the load is shared by the spring and the bar,
and the force displacement curve changes. During this portion of
the loading, plastic deformation of the NiTi takes place, and the
force displacement curve is reversible. As a greater load is
applied, the force displacement curve becomes irreversible. Thus,
the energy absorbing structure can be reused after the application
of relatively modest loads, but must be replaced after the
application of greater loads.
[0009] Other embodiments of the energy absorbing structure include
additional SMA springs and additional porous SMA bars. The energy
absorbing structure as disclosed herein can be beneficially
incorporated, for example, into airborne vehicles, ground vehicles,
and seagoing vehicles, to reduce impact loading under a variety of
circumstances. An additional application involves using energy
absorbing structures generally consistent with those described
above for ballistic protection for military vehicles, military
personnel, and law enforcement personnel.
[0010] In one embodiment of an energy absorbing structure, as an
SMA spring is compressed, a porous SMA element is exposed to a
load, and as the porous SMA element is loaded, the porous SMA
contacts the SMA spring. This configuration is substantially like a
pillar with a side constraint. The function of the side constraint
is to increase the buckling load that the porous SMA element can
withstand. A plurality of such pillars can be used together to
achieve a dampening mechanism for implementation in vehicles, for
example, in energy absorbing automotive bumpers. The energy
absorbing properties of such a structure can also be beneficially
used in medical devices and in many other applications.
[0011] This Summary has been provided to introduce a few concepts
in a simplified form that are further described in detail below in
the Description. However, this Summary is not intended to identify
key or essential features of the claimed subject matter, nor is it
intended to be used as an aid in determining the scope of the
claimed subject matter.
DRAWINGS
[0012] Various aspects and attendant advantages of one or more
exemplary embodiments and modifications thereto will become more
readily appreciated as the same becomes better understood by
reference to the following detailed description, when taken in
conjunction with the accompanying drawings, wherein:
[0013] FIG. 1 schematically illustrates an SPS system;
[0014] FIG. 2 is a flow chart showing exemplary steps to form a
porous SMA using SPS;
[0015] FIG. 3A is an image of the microstructure of a NiTi specimen
exhibiting a 25% porosity;
[0016] FIG. 3B is an image of the microstructure of a NiTi specimen
exhibiting a 13% porosity;
[0017] FIG. 3C is an image of a porous NiTi disk formed using
SPS;
[0018] FIG. 3D is an enlarged image of a portion of the porous NiTi
disk of FIG. 3C;
[0019] FIG. 3E is an image of the porous NiTi disk of FIG. 3C
processed into desirable shapes using electro discharge machining
(EDM);
[0020] FIG. 4A graphically illustrates the compressive
stress-strain curves of a dense NiTi specimen, the 25% NiTi
specimen of FIG. 3A, and the 13% NiTi specimen of FIG. 3B, when
tested at room temperature;
[0021] FIG. 4B graphically illustrates the compressive
stress-strain curves of a dense NiTi specimen and the 13% NiTi
specimen of FIG. 3B tested at temperatures greater than their
austenite finish temperatures;
[0022] FIGS. 5A-5C are optical micrographs of samples of the 13%
porosity NiTi specimen;
[0023] FIG. 6A graphically illustrates an idealized compressive
stress-strain curve, including a super elastic loop, for both dense
NiTi and porous NiTi;
[0024] FIG. 6B graphically illustrates a linearized compressive
stress-strain curve (based on FIG. 6A), including three distinct
stages, for both dense NiTi and porous NiTi;
[0025] FIG. 6C graphically compares the stress and strain curves
for the dense NiTi and the 13% porous NiTi, and a stress and strain
curve predicted using a model based on FIG. 6B;
[0026] FIG. 7A is an image of an energy absorbing structure that
includes a porous NiTi rod, and a NiTi spring;
[0027] FIG. 7B schematically illustrates an energy absorbing
structure including a porous NiTi rod and a NiTi spring;
[0028] FIGS. 7C and 7D schematically illustrate dimensions for
exemplary energy absorbing structures including a porous NiTi rod
and a NiTi spring;
[0029] FIGS. 8A-8C schematically illustrate an energy absorbing
structure in accord with those described herein under various
loading conditions;
[0030] FIG. 9A graphically illustrates a force displacement curve
of a single porous NiTi rod;
[0031] FIG. 9B graphically illustrates a force displacement curve
of the exemplary energy absorbing structure of FIGS. 7A and 7B;
[0032] FIG. 10A schematically illustrates an energy absorbing
structure including a plurality of porous NiTi rods and NiTi
springs; and
[0033] FIGS. 10B and 10C schematically illustrate an energy
absorbing structure including a single porous NiTi rods and a
plurality of NiTi springs.
DESCRIPTION
Figures and Disclosed Embodiments are not Limiting
[0034] Exemplary embodiments are illustrated in referenced Figures
of the drawings. It is intended that the embodiments and Figures
disclosed herein are to be considered illustrative rather than
restrictive.
Overview
[0035] The disclosure provided herein encompasses a method for
producing a ductile porous SMA using SPS, a model developed to
predict the properties of a porous SMA, and an energy absorbing
structure that includes a generally nonporous SMA portion and a
porous SMA portion, to achieve a lightweight energy absorbing
structure having desirable properties.
Production of a Ductile and Porous SMA Using SPS
[0036] One advantage of using SPS to generate a porous SMA is that
strong bonding among super elastic grade SMA powders can be
achieved relatively quickly (i.e., within about five minutes) using
a relatively low sintering temperature, thereby minimizing the
production of undesirable reaction products, which often are
generated using conventional sintering techniques.
[0037] SPS uses a combination of heat, pressure, and pulses of
electric current, and generally operates at lower temperatures than
the conventional sintering techniques discussed above. The SPS
method comprises three main mechanisms: (1) the application of
uni-axial pressure; (2) the application of a pulsed voltage; and
(3) the heating of the pressure die (generally a graphite die) and
the sample. FIG. 1 schematically illustrates an exemplary SPS
system 10, including an upper electrode 12a, an upper punch 22a, a
carbon die 14, a sample chamber 18, a thermocouple 16, a lower
electrode 12b, a lower punch 22b, a vacuum chamber 20, and a power
supply 24. SPS equipment is commercially available from several
sources, such as Sumitomo Coal Mining Co. Ltd., Japan (the Dr.
Sinter SPS-515S.TM., and the Dr. Sinter 2050.TM.) and FCT System
GmbH, Germany (the FCT--HP D 25/1.TM.).
[0038] Significantly, the SPS technique has a short cycle time
(e.g., cycle times of a few minutes are common), since the tool and
components are directly heated by DC current pulses. The DC pulses
also lead to an additional increase of the sintering activity with
many materials, resulting from processes that occur on the points
of contact of the powder particles (i.e., Joule heating, generation
of plasma, electro migration, etc.). Therefore, significantly lower
temperatures, as well as significantly lower mold pressures, are
required, compared to conventional sintering techniques.
[0039] FIG. 2 is a flowchart 50 showing exemplary steps that can be
carried out to produce a porous SMA component using SPS. In a step
52, a powdered SMA is loaded into the SPS system of FIG. 1. In a
step 54, the SPS system is used to sinter the powder employing a
combination of pressure, electrical current, and heat (the heat is
generally provided by the electrical current, but other heat
sources can be used, as long as the thermal effects of the current
are accounted for), generating a porous SMA disk. Exemplary
processing conditions for NiTi powders are provided below in Table
1. While sintering dies often generate disks, it should be
recognized that sintering dies (and the pressure die in the SPS
system) can be configured to produce other shapes, thus, the
present invention is not limited to the production of a single
shape.
[0040] In a step 56, the porous SMA disk is processed into more
desirable shapes. As described in greater detail below, SMA
cylinders can be beneficially employed to produce an energy
absorbing structure. Thus, step 56 indicates that the porous SMA
disk is processed to generate a plurality of cylinders. Further,
step 56 indicates that the processing is performed using EDM.
However, it should be recognized that other shapes, and other
processing techniques, can be used to produce a desired shape. In a
step 58, the porous SMA cylinders are heat treated to ensure that
the SMA cylinders are super elastic. An exemplary heat treatment
for porous NiTi is to heat the components at about 300.degree.
C.-320.degree. C. for about 30 minutes, followed by an ice water
quench.
[0041] The method steps described in connection with FIG. 2 are
exemplary, and it should be understood that they can be modified as
desired. For example, if the SPS die is configured to achieve the
component shape desired, step 56 can be eliminated. Further, if
super elastic grade components are not required, the heat treatment
of step 58 can be eliminated.
Empirical Processing of NiTi Specimens Using SPS
[0042] Several different studies have been performed to validate
the ability of SPS to achieve a ductile and porous SMA. In one
study, an ingot of NiTi alloy (Ni (50.9 at. wt. %) and Ti (49.1 at.
wt. %); provided by Sumitomo Metals, Osaka, Japan) was processed
into powder form using plasma rotating electrode processing (PREP).
The average diameter of the NiTi powders processed by PREP is about
150 .mu.m. As noted above, one advantage of the SPS technique is to
provide strong bonding among super elastic grade powders (such as
NiTi) while a relatively low sintering temperature is maintained
for a relatively short time (such as 5 minutes), thus avoiding any
undesired reaction products that would be produced by a
conventional sintering method.
[0043] A summary of three types of specimens processed is provided
in Table 1. Each specimen was subjected to the same heat treatment
(320.degree. C., 30 min, water quench) to convert them to super
elastic grade. Their transformation temperatures were measured
using a differential scanning calorimeter chart (Perkin-Elmer,
DSC6.TM. model): A.sub.s (austenite start), A.sub.f (austenite
finish), M.sub.s (martensite start) and M.sub.f (martensite
finish). TABLE-US-00001 TABLE 1 NiTi Specimens Processed by Spark
Plasma Sintering Porosity Transformation Sample by volume SPS
Conditions Temp. (.degree. C.) Dense NiTi 0 850.degree. C. under
A.sub.s = 23.88, A.sub.f = 43.12 50 MPa, 5 min M.sub.s = 36.05,
M.sub.f = 23.09 13% porous NiTi 13% 800.degree. C. under A.sub.s =
19.3, A.sub.f = 38.82 25 MPa, 5 min M.sub.s = 20.65, M.sub.f = 5.39
25% porous NiTi 25% 750.degree. C. under A.sub.s = 14.59, A.sub.f =
33.29 5 MPa, 5 min M.sub.s = 23.24, M.sub.f = 2.55
[0044] The porosity of the specimens was measured using the
formula, f.sub.p=1-M/(.rho.V), where V and m are respectively the
volume and mass of the porous specimen. The density .rho. is the
density of NiTi (i.e., 6.4 g/cm.sup.3) as measured by the
mass-density relationship .rho.=m.sub.D/V.sub.D. The unit of .rho.
is g/cm.sup.3, and V.sub.D and m.sub.D are respectively the volume
and mass of the dense NiTi specimen. The porous specimens exhibited
a functionally graded microstructure, in that NiTi powders of
smaller size are purposely distributed near the top and bottom
surfaces while the larger sized NiTi powders are located in
mid-thickness region, as indicated in FIG. 3A (an image of the 25%
porosity NiTi), and FIG. 3B (an image of the 13% porosity NiTi).
The 13% porosity NiTi specimen exhibited continuous NiTi phase
throughout its thickness, with porosity centered at mid-plane (as
indicated by an area 28), while in the 25% porosity specimen,
porosity is distributed throughout the thickness, with less
porosity towards the top and bottom surfaces ("top" and "bottom"
being relative to the specimen as shown).
[0045] FIG. 3C is an image of a porous NiTi disk fabricated using
SPS, while FIG. 3D is an enlarged image of a portion of the NiTi
disk. FIG. 3E shows how the disk was processed using EMD to form
porous NiTi/SMA cylinders. The NiTi cylinders were tested as
described below.
[0046] Two types of compressive tests were conducted (using an
Instron tensile frame; model 8521.TM.) to obtain the stress-strain
curves of both the dense and the porous (25% and 13%) NiTi. Two
different testing temperatures were used: (1) room temperature
(22.degree. C.); and (2) a temperature 15-25.degree. C. higher than
the austenite finish temperature (A.sub.f) of the specimen. The
porous specimens, with porosities of 13% and 25%, and the dense
specimen were each tested under a static compressive load (loading
rate 10.sup.-5 s.sup.-1). The results are graphically illustrated
in FIG. 4A. The 25% porosity NiTi specimen exhibits the lowest flow
stress level and the least super elastic loop behavior, while both
the 13% porosity NiTi specimen and the dense NiTi specimen clearly
exhibit larger super elastic loops, and greater ductility. The main
reason for the better super elastic behavior of the 13% porosity
NiTi specimen processed by SPS technique described above is the
rather continuous connectivity between adjacent NiTi powders of
super elastic grade in the high porosity region (mid-section). In
the case of the 25% porosity NiTi specimen, such connectivity is
not established in the mid-section( i.e., there is non-uniform
connectivity). In addition, the 25% porosity NiTi specimen appears
to include clusters of NiTi powder particles, which at least in
part have converted to undesirable brittle inter-metallics. Such
conversion can occur due to hot spots in the NiTi powder during the
SPS process. When stress is sufficiently large, the collapse of
imperfect necking structures among large NiTi particles in the 25%
porosity specimen leads to the specimen exhibiting a relatively low
strength, rather than the desired super elasticity. Based on the
results of the compression testing, the 13% porosity specimen was
selected for further testing.
[0047] FIGS. 5A-5C are optical micrographs of samples of the 13%
porosity NiTi specimen. FIG. 5A is an optical micrograph of a
sample of the 13% porosity NiTi specimen before the compression
test. FIG. 5B is an optical micrograph of a sample of the 13%
porosity NiTi specimen after being loaded to achieve a 5%
compression, and subsequent unloading. FIG. 5C is an optical
micrograph of a sample of the 13% porosity NiTi specimen after
being loaded to achieve a 7% compression, and subsequent unloading.
FIG. 5B indicates that the 13% porosity NiTi remains super elastic
when compressed to about 5%, because after unloading, the material
returns to the uncompressed configuration shown in FIG. 5A. In
contrast, FIG. 5C indicates that the 13% porosity NiTi undergoes
plastic deformation when compressed to about 7%. This behavior is
due to the material being in the martensitic phase.
[0048] FIGS. 5A and 5B support the conclusion that the 13% porosity
NiTi specimen processed as described above (SPS followed by heat
treatment) deforms super elastically, contributing to its high
ductility. On the other hand, the microstructure of the 25%
porosity sample exhibits a markedly different microstructure, which
appears to explain why the compressive stress-strain curve of the
25% porosity NiTi exhibits a much lower flow stress.
[0049] As noted above, compression testing was performed both at
room temperature, and at a temperature greater than the austenite
finish temperature of the material. FIG. 4B graphically illustrates
the compressive stress-strain curves of the 13% porosity NiTi
specimen and the dense NiTi specimen. The compressive stress-strain
curves tested at T>A.sub.f more clearly exhibit a super elastic
loop at higher flow stress level when compared to the compressive
stress-strain curves tested at room temperature (FIG. 4A). This
result is due to the fact that NiTi exhibits super elastic behavior
at higher flow stress levels, at higher temperatures.
Modeling of the Compressive Stress-Strain Curves of Porous NiTi
[0050] In order to optimally design the microstructure and
properties of porous SMAs, it is important to develop a simple, yet
accurate model to describe the microstructure and mechanical
behavior relationships of porous SMAs. If a porous NiTi is treated
as a special case of a particle-reinforced composite, a
micromechanical model can be applied that is based on Eshelby's
method with the Mori-Tanaka mean-field (MT) theory and the
self-consistent method. Both methods have been used to model
macroscopic behavior of composites with SMA fibers. Young's modulus
of a porous material was modeled by using the Eshelby's method with
MT theory.
[0051] Eshelby's equivalent inclusion method combined with the
Mori-Tanaka mean-field theory can thus be used to predict the
stress-strain curve of a porous NiTi under compression, while
accounting for the super elastic deformation corresponding to the
second stage of the stress-strain curve. The predicted
stress-strain curve can be compared with the experimental data of
the porous NiTi specimen processed by SPS.
[0052] The model assumes a piecewise linear stress-strain curve of
super elastic NiTi. FIG. 6A graphically illustrates an idealized
compressive stress-strain curve, including a super elastic loop,
for both dense NiTi and porous NiTi. FIG. 6B graphically
illustrates a linearized compressive stress-strain curve (based on
FIG. 6A), including three distinct stages, for both dense NiTi and
porous NiTi. FIG. 6C graphically illustrates stress and strain
curves for the dense NiTi and the porous NiTi, and a stress and
strain curve predicted using the model described in detail
below.
[0053] Referring to the idealized stress-strain curve of FIG. 6B, a
first linear part, A.sub.iB.sub.i, corresponds to the elastic
loading of the 100% austenite phase. A second linear part,
B.sub.iD.sub.i, corresponds to the stress-induced martensite
transformation plateau. D.sub.id.sub.i corresponds to the unloading
of the 100% martensite phase, and d.sub.ib.sub.i corresponds to the
reverse transformation lower plateau. A final linear part is
b.sub.iA.sub.i which corresponds to the elastic unloading of the
100% austenite phase. The subscript "i" in FIG. 6B denotes both
dense (i=D) and porous NiTi (i=P), since the idealized curve
applies to both cases.
[0054] The stress-strain curve of FIG. 6A includes both a loading
curve and an unloading curve, which collectively generate the
characteristic super elastic loop. Models for the loading curve and
unloading curve are discussed below.
[0055] With respect to a model for the loading curve, the
compressive stress-strain curve of the 13% porosity specimen of
FIG. 4B exhibits three stages (as indicated in FIG. 6B and as
discussed above): first stage A.sub.iB.sub.i (the 100% austenite
phase); second stage B.sub.iD.sub.i (the upper plateau,
corresponding to the stress-induced martensite phase); and third
stage D.sub.id.sub.i (the 100% martensite phase). Although the
compressive stress-strain curves for these three stages shown in
FIG. 4B do not completely correspond to the linear stages shown in
FIG. 6B, for the purposes of modeling the loading curve for the 13%
porosity specimen of NiTi, it can be assumed that each stage is
linear. Using that assumption, a simple model of the three
piecewise linear stages can be based on Eshelby's effective medium
model and the Mori-Tanaka mean-field theory. The slopes of the
linearized first, second, and third stages of the 13% porous NiTi
specimen are respectively defined as E.sub.Ms, E.sub.T, and
E.sub.Mf, where the subscripts M.sub.s, T, and M.sub.f respectively
denote the first stage with the martensite phase start (equivalent
to the 100% austenite phase), the second stage linearized slopes
with tangent modulus, and the third stage with the martensite
finish (i.e., the 100% martensite phase). The stresses at the
transition between the first and second stages and between the
second and third stages are denoted
[0056] by .sigma..sub.M.sup.P, and .sigma..sub.M.sub.f.sup.P,
respectively, where the superscript `P` denotes the porous NiTi.
Therefore, the calculation of the moduli E.sub.M.sub.s, E.sub.T,
and E.sub.M.sub.f, as well as the martensitic transformation start
stress, .sigma..sub.M.sup.P, and the martensitic transformation
finish stress, .sigma..sub.M.sub.f.sup.P, are the keys to this
model.
[0057] Note that with respect to the model for the unloading
portion of the stress-strain curve discussed below, no uniform
strain and stress in the matrix NiTi is assumed. With respect to
determining critical stresses, note that the start and finish
martensitic transformation stresses .sigma..sub.M.sub.s.sup.P and
.sigma..sub.M.sub.f.sup.P can be obtained using the relationships
in Eq. (1a) and Eq. (1b), which follow: .sigma. M s P = ( 1 - f p )
.times. .sigma. M s D , ( 1 .times. a ) .sigma. M f P = ( 1 - f p )
.times. .sigma. M f D , ( 1 .times. b ) ##EQU1## where
.sigma..sub.M.sub.s.sup.D and .sigma..sub.M.sub.f.sup.D are
respectively, the start and finish martensitic transformation
stresses that are averaged in the matrix domain.
[0058] To determine the stiffness of the first and third stages, a
formula based on Eshelby's model and the Mori-Tanaka mean-field
theory can be used to calculate the Young's modulus of a porous
material, as follows: E P E D = 1 1 + nf p , ( 2 ) ##EQU2## where
for spherical pores, .eta. is given by n = 15 7 .times. ( 1 - f p )
, ( 3 ) ##EQU3## A brief derivation of Eqs. (2) and (3) is provided
in Appendix A.
[0059] Determination of the stiffness of the second stage can be
obtained as follows. The Young's modulus (E) of a NiTi with
transformation .epsilon..sub.T is estimated by: E .function. ( T )
= E A + T _ .times. ( E M - E A ) , ( 4 ) ##EQU4## where E.sub.A
and E.sub.M are respectively the Young's modulus of the 100%
austenite and the 100% martensite phase, and .epsilon. is the
maximum transformation strain, which can be obtained using the
following relationship: _ = M f - .sigma. M f E M , ( 5 )
##EQU5##
[0060] Eq. (4) is valid for both the dense and the porous NiTi
(13%); thus, Eqs. (4) and (5) can be rewritten as follows: E i = E
A i - E A i - E M i M f i - .sigma. M f i / E M i .times. T , ( 6 )
##EQU6## where the superscript `i` denotes i=D (dense) or P
(porous). In order to obtain the slope of the linearized second
stage of the compressive stress-strain curve of a porous NiTi, the
equivalency of the strain energy density must be considered.
However, in the case of the second stage, the macroscopic strain
energy density of porous NiTi should be evaluated from the
trapezoidal area of FIG. 6B, i.e., the trapezoid
B.sub.iC.sub.iF.sub.iH.sub.i, where i=P for an arbitrary
transformation strain .epsilon..sub.T.sup.P. Therefore, the
macroscopic strain energy density of porous NiTi with
.epsilon..sub.T.sup.P calculated graphically from FIG. 6C is given
by: W = 1 2 .times. ( .sigma. M s P + .sigma. 0 P ) .times. ( T P +
.sigma. 0 P E AM - .sigma. M s P E M s ) , ( 7 ) ##EQU7## where
.sigma..sub.M.sub.s.sup.P is the start martensitic transformation
stress of the porous NiTi material, .sigma..sub.0.sup.P is an
applied stress, and .epsilon..sub.T.sup.P is the strain
corresponding to .sigma..sub.0.sup.P (see FIG. 6B). Since there is
no transformation strain in pores, the transformation strain for
porous NiTi, .epsilon..sub.T.sup.P, is the uniform transformation
strain in the dense NiTi, .epsilon..sub.T.sup.D. Thus,
.epsilon..sub.T.sup.P=.epsilon..sub.T.sup.D.ident..epsilon..sub.T,
(8)
[0061] The macroscopic strain energy density determined above is
set equal to the microscopic strain energy density, which is
calculated using Eshelby's inhomogeneous inclusion method, such
that: W = 1 2 .times. C ijkl m - 1 .times. .sigma. ij 0 .times.
.sigma. kl 0 + 1 2 .times. f P .times. .sigma. ij 0 .times. kl * ,
( 9 ) ##EQU8## where the corresponding Eshelby's problem provides
the solution for .epsilon..sub.ij* as: kl * = kl T - 1 1 - f P
.times. ( S klmn - I ) - 1 .times. C ijkl m - 1 .times. .sigma. ij
0 , ( 10 ) ##EQU9##
[0062] Substituting Eq. (10) into Eq. (9), the microscopic strain
energy density, W, is given by: W = 1 2 .times. .sigma. ij 0
.times. ij 0 + 1 2 .times. f P .times. .sigma. ij 0 .function. [ 2
.times. ij T - 1 1 - f P .times. ( S ijkl - I ) - 1 .times. kl 0 ]
, ( 11 ) ##EQU10##
[0063] Since the porous NiTi is subjected to uni-axial load (i.e.,
.sigma..sub.ij.sup.0={0,0,.sigma..sub.0.sup.P,0,0,0}.sup.T, and
.epsilon..sub.ij.sup.T={.nu..epsilon..sub.T,.nu..epsilon..sub.T-.epsilon.-
.sub.T,0,0,0}.sup.T, ), and the pores are assumed to be spherical,
Eq. (11) can be reduced to: W = 1 2 .times. .sigma. 0 P .times. 0 +
1 2 .times. f P .times. .sigma. 0 P .function. [ 2 .times. T + 15 7
.times. ( 1 - f P ) .times. 0 ] , ( 12 ) ##EQU11## where
.epsilon..sub.0 is the macroscopic strain of the porous NiTi, and
it is related to applied stress .sigma..sub.0.sup.P as: 0 = .sigma.
0 P E AM , ( 13 ) ##EQU12##
[0064] Substituting Eq. (13) into Eq. (12), the microscopic strain
energy density W of the porous NiTi is finally reduced to: W = 1 2
.times. ( .sigma. 0 P ) 2 E AM + 1 2 .times. f P .times. .sigma. 0
P .function. [ 2 .times. T P - 15 7 .times. ( 1 - f P ) .times.
.sigma. 0 P E AM ] , ( 14 ) ##EQU13## where E.sub.AM is the Young's
modulus of dense (matrix) NiTi with .epsilon..sub.T.
[0065] By equating the macroscopic strain energy density of Eq. (7)
to the microscopic strain energy density of Eq. (14), and using Eq.
(6) with i=P, an algebraic equation of second-order in terms of
.epsilon..sub.T is obtained, as follows: A .function. ( T ) 2 + B
.times. .times. T + C = 0 , .times. where .times. .times. A = (
.gamma..sigma. 0 P + .sigma. M s P ) .times. ( 1 - .beta. ) M s ,
.times. B = .gamma..sigma. 0 p + .sigma. M s P + .sigma. M s P
.function. ( 1 - .beta. ) .times. ( .sigma. M s P + .sigma. 0 P ) E
M s .times. M f , .times. C = ( 1 - .alpha. ) .times. ( .sigma. 0 P
) 2 - ( .sigma. M s P ) 2 E M s .times. .times. and .times. .times.
.alpha. = 1 - f p 1 - f P .times. ( S 3333 - 1 ) - 1 , .beta. = E M
f E M s , .gamma. = 1 - 2 .times. .times. f P , ( 15 )
##EQU14##
[0066] Solving for .epsilon..sub.T.sup.P, which corresponds to the
second kink point, D.sub.P of FIG. 6B (i.e., see D.sub.i), the
following is obtained: T = - B + B 2 - 4 .times. AC 2 .times. A , (
16 ) ##EQU15##
[0067] The tangent modulus of the porous NiTi is the slope of the
second portion of the stress-strain curve shown in FIG. 6B, thus,
E.sub.T can be expressed in terms of transformation strain and the
stresses: E T = .sigma. 0 P - .sigma. M s P T , ( 17 )
##EQU16##
[0068] Referring now to the unloading curve portion of the
idealized stress-strain curve of FIG. 6B, note that during
unloading, the porous NiTi material undergoes transformation (from
the martensite phase to the austenite phase).
[0069] Before the applied stress reaches the critical value
.sigma..sub.A.sub.s.sup.P, the matrix of the NiTi remains in a 100%
martensite phase (the first stage of the unloading stress-strain
curve in the modeling curve).
[0070] When the applied stress is decreased to
.sigma..sub.A.sub.s.sup.P, reverse transformation begins. The
reverse transformation finishes when the stress reaches another
critical value, .sigma..sub.A.sub.f.sup.P, thereafter the porous
NiTi material remains 100% austenite.
[0071] Therefore, the slopes of the first and third stages of the
unloading curve are the Young's moduli of the 100% martensite and
the 100% austenite phase, respectively. The slope of the second
stage is the same as that of the loading curve. Therefore, the
Young's moduli of the unloading curve are related to those of the
loading curve as: E.sub.A.sub.s=E.sub.M.sub.f (18a)
E.sub.T.sup.u=E.sub.T, (18b) E.sub.A.sub.f=E.sub.M.sub.s, (18c)
where .epsilon..sub.T.sup.u is the slope of the second stage of the
unloading curve. The superscript `u` denotes unloading, and the
components without superscripts are the slopes of loading
curve.
[0072] The start and finish austenite transformation stresses of
porous NiTi, .sigma..sub.A.sub.s.sup.P and
.sigma..sub.A.sub.f.sup.P are related to the corresponding stresses
of the dense NiTi:
.sigma..sub.A.sub.s.sup.P=(1-f.sub.P).sigma..sub.A.sub.s.sup.D,
(19a)
.sigma..sub.A.sub.f.sup.P=(1-f.sub.P).sigma..sub.A.sub.f.sup.D,
(19b)
[0073] where .sigma..sub.A.sub.s.sup.D and
.sigma..sub.A.sub.f.sup.P are respectively the start and finish
austenite transformation stresses of the dense NiTi. First, it is
assumed that the dense NiTi matrix is isotropic, with a Poisson's
ratio .nu..sup.A=.nu..sup.M=0.33. Input data measured from the
idealized compressive stress-strain curve of FIG. 4B are shown in
Table 2. TABLE-US-00002 TABLE 2 Input Data
.sigma..sub.M.sub.s.sup.D (MPa) .sigma..sub.M.sub.f.sup.D(MPa)
.sigma..sub.A.sub.f.sup.D(MPa) E.sub.A (GPa) E.sub.M
.epsilon..sub.M.sub.s .epsilon..sub.M.sub.f 400 720 300 75 31 0.004
0.032
[0074] In the empirical testing of the porous and solid NiTi
specimens discussed above, SPS was used to generate porous NiTi
exhibiting two different porosities, 13% and 25%. The 13% porosity
NiTi appears to possess a desirable microstructure with a high
ductility, while the 25% porosity NiTi specimens exhibits a much
lower stress flow than that of the 13% porosity. The piecewise
linear stress-strain curve model of the compressive stress-strain
curve of the 13% porosity NiTi discussed above predicts the flow
stress level of the experimental stress-strain curve reasonably
well.
An Energy Absorbing Structure Incorporating Porous NiTi
[0075] Having successfully fabricated a porous SMA having good
ductility using SPS (the 13% porosity NiTi discussed in detail
above), an energy absorbing structure incorporating a porous,
ductile and super elastic SMA was designed. The energy absorbing
structure includes an SMA member and a porous SMA member.
[0076] FIG. 7A is an image of an exemplary energy absorbing
structure, including a porous NiTi cylinder 32 and a NiTi spring
34. FIG. 7B schematically illustrates an exemplary configuration,
while FIGS. 7C and 7D provide details of exemplary dimensions
(although it should be understood that such dimensions are not
intended to be limiting). While NiTi represents an exemplary SMA
for the spring element, and porous NiTi represents an exemplary
porous SMA for the rod/cylinder element, it should also be apparent
that the implementation of NiTi for either element is not intended
to be limiting. Furthermore, while the spring/cylinder (or
spring/rod) configuration is desirable, in that the spring provides
a side constraint to increase the buckling load that can be applied
to the rod/cylinder, other configurations in which a first SMA
element provides a side constraint to a second SMA element can also
be implemented. Thus, the SMA element providing a side constraint
can be implemented in structural configurations not limited to
spring 34, and the second SMA element (the element benefiting from
the side constraint) can be implemented using structures other than
a rod/cylinder.
[0077] The concept of the SMA composite structure of FIGS. 7A-7D is
to provide a structure that behaves super-elastically for modest to
intermediate impact loading (and is thus reusable for future impact
loadings), and which also can adsorb larger loads, particularly
after the porous cylinder swells horizontally, thus touching the
outer spring. FIGS. 8A-8C schematically illustrate the exemplary
energy absorbing structure under loading. In FIG. 8A, an initial
load is received by NiTi spring 34. In FIG. 8B, the load has caused
spring 34 to compress, and part of the load is now applied to
cylinder 32 as well. In FIG. 8C, additional loading causes cylinder
32 to deform, such that the walls of the cylinder touch the spring
(which provides a side constraint to the cylinder, increasing the
buckling load that can be absorbed by the cylinder).
[0078] FIG. 9A graphically illustrates a force displacement curve
of a single porous NiTi rod, while FIG. 9B graphically illustrates
a force displacement curve of the exemplary energy absorbing
structure of FIGS. 7A and 7B. Obviously, the energy absorbing
structure of FIGS. 7A and 7B is able to support a larger force and
displacement. For the porous NiTi rod, the spring plays a role as a
constraint, and the porous NiTi rod and surrounding spring (i.e.,
the exemplary energy absorbing structure) exhibits a higher super
elastic force, a higher fracture point and larger displacement than
does the porous NiTi rod without the spring. On the other hand, the
porous NiTi rod acts as a yoke for the spring, preventing it from
asymmetric deformation (i.e., premature buckling) when subjected to
large force.
[0079] The following discussion of FIGS. 9A and 9B relates to the
energy absorbing (EA) capacity under reversible loading (i.e.,
super elastic loading) and irreversible loading (loading all the
way to a fracture point) of selected specimens. For reversible
loading, EA is defined as the area encompassed by the super elastic
loop, while for irreversible loading, EA is defined as the area
under the force-displacement curve up, to the fracture point marked
in each Figure by an X. The two values of EA are divided by the
mass of each specimen to calculate a specific EA. Key mechanical
data (including specific EAs) are listed in Tables 3 and 4. The
data (and FIGS. 3A and 3B) demonstrate the advantage of using the
composite structure (i.e., the exemplary energy absorbing structure
of FIGS. 7A and 7B) rather than employing a porous NiTi rod without
a constraint, to cope with a wide range of compressive loads.
[0080] FIG. 10A schematically illustrates an energy absorbing
structure 40 including a plurality of substructures 42, each
substructure including a porous NiTi rod and a plurality of NiTi
springs. FIGS. 10B and 10C provide details of the configuration of
substructures 42. TABLE-US-00003 TABLE 3 Comparison of Experimental
Data for a Single Porous NiTi Rod and the Exemplary Energy
Absorbing Structure Maximum Maximum Reversible Reversible Fracture
Fracture Specific Energy Displacement Force Displacement Force
Absorption Single Porous 1.29 mm 40.74 KN 2.03 mm 65.15 KN 12.2
MJ/Mg NiTi Rod Exemplary 7.01 mm 68.76 KN 7.71 mm 97.21 KN 15.3
MJ/Mg Structure
[0081] TABLE-US-00004 TABLE 4 Comparison of the Specific EA of
Various Materials 13% porosity Composite Materials AlCu.sub.4 Foam
Al w/Si added Al NiTi rod structure NRG Absorption 5.2 4.2 20 68.3
141.5 (MJ/m.sup.3)
[0082] In summary, the exemplary energy absorbing structure has a
dual use as an efficient energy absorber, for both reversible low
impact loadings and irreversible high impact loadings. It is noted
also that the higher strain-rate impact loading, the higher the
flow stress of NiTi becomes, which may be considered an additional
advantage of using NiTi as a key energy absorbing material.
[0083] In yet another embodiment, the spring is made from
conventional materials, and only the inner rod/cylinder is a SMA.
The energy absorbing capability of such an embodiment has yet to be
investigated.
[0084] Although the present invention has been described in
connection with the preferred form of practicing it and
modifications thereto, those of ordinary skill in the art will
understand that many other modifications can be made to the present
invention within the scope of the claims that follow. Accordingly,
it is not intended that the scope of the invention in any way be
limited by the above description, but instead be determined
entirely by reference to the claims that follow.
Appendix A
[0085] The Eshelby's inhomogeneous inclusion problem with the
Mori-Tanaka mean-field theory provides the total stress field is
given by: .sigma. ij 0 + .alpha. .times. .times. ij = C ijkl m
.function. [ kl 0 + _ kl + kl - ( kl * - kl T ) ] = C ijkl m
.function. ( kl 0 + _ kl + kl - kl ** ) = C ijkl p .function. ( kl
0 + _ kl + kl ) ( A .times. .times. 1 ) ##EQU17## where
C.sub.ijkl.sup.m and C.sub.ijkl.sup.P are respectively the elastic
stiffness tensor of matrix and pores; .sigma..sub.ij and
.epsilon..sub.kl are respectively the stress disturbance and the
strain disturbance due to the existence of pores; .epsilon..sub.kl
is the average strain disturbance in the matrix due to the pores;
and .epsilon..sub.ij* is a fictitious eigen strain which has
non-vanishing components. To facilitate solving Eshelby's formula,
.epsilon..sub.kl**, defined below in Eq. (A2), is introduced.
.epsilon..sub.kl**=.epsilon..sub.kl*-.epsilon..sub.kl.sup.T,
(A2)
[0086] For the entire composite domain, the following relationship
always holds:
.sigma..sub.ij.sup.0=C.sub.ijkl.sup.m.epsilon..sub.kl.sup.0,
(A3)
[0087] From Eshelby's equation, the strain disturbance is related
to .epsilon..sub.mn** as:
.epsilon..sub.kl=S.sub.klmn.epsilon..sub.mn**, (A4)
[0088] The requirement that the integration of the stress
disturbance over the entire body vanishes leads to:
.epsilon..sub.kl=-f.sub.P(S.sub.klmn.epsilon..sub.mn**-.epsilon..sub.kl**-
1). (A5)
[0089] S.sub.klmn is the Eshelby's tensor for pores derived in
Appendix B (below). A substitution of Eqs. (A3), (A4), and (A5)
into Eq. (A1), and use of C.sub.ijkl.sup.P=0 (due to the pores)
provides the following solution for .epsilon..sub.kl**, kl ** = - 1
1 - f p .times. ( S klmn - I ) - 1 .times. C ijkl - 1 .times.
.sigma. ij 0 . ( A .times. .times. 6 ) ##EQU18##
[0090] The equivalency of the strain energy density of the porous
NiTi leads to: .sigma. 0 2 2 .times. E P = .sigma. 0 2 2 .times. E
D + f p 2 .times. .sigma. 0 .times. 33 ** , ( A .times. .times. 7 )
##EQU19## where the applied stress .sigma..sub.0 is assumed to be
along x.sub.3-axis.
Appendix B
Eshelby's Tensor for Sphere Inclusion
[0091] S 1111 = S 2222 = S 3333 = 7 - 5 .times. .times. v 15
.times. ( 1 - v ) , .times. S 1122 = S 2233 = S 3311 = S 2211 = S
3322 = 5 .times. .times. v - 1 15 .times. ( 1 - v ) , .times. S
1212 = S 2323 = S 3131 = 4 - 5 .times. .times. v 15 .times. .times.
( 1 - v ) , ##EQU20##
* * * * *